Intergenerational Wealth Mobility:
Evidence from Danish Wealth Records of Three Generations
Simon Halphen Boserup
University of Copenhagen
Wojciech Kopczuk
Columbia University, CEPR, and NBER
Claus Thustrup Kreiner
University of Copenhagen and CEPR
March 2013
Abstract
We provide empirical evidence on the intergenerational mobility of wealth using administrative wealth records of three generations of Danes. Our preferred estimate for the intergenerational wealth elasticity (IWE) is 0.2 (and 0.27 when limiting attention to those with
positive wealth only). We construct a theoretical framework that allows for understanding
the variability of the IWE across time, samples, and countries. Our framework highlights
that the IWE can be interpreted as the weighted average of elasticities corresponding to different sources of intergenerational correlation that may in principle vary in importance across
di¤erent contexts. However, we …nd that the IWE is surprisingly stable when estimated for
di¤erent age groups, when using parents-grandparents pairs instead of children and parents,
when eliminating bequests, and when explicitly shutting down many of the potential channels
behind intergenerational wealth mobility, including income and education. This suggests that
parental wealth is a su¢ cient statistic for the channels that we control for and those that
vary across di¤erent samples, that is, the e¤ect of these parental characteristics on wealth of
children can be summarized by their e¤ect on wealth of parents. By exploiting information
for three generations we …nd that the standard child-parents elasticity severely underestimates the long-term persistence in the formation of wealth across generations. We show that
either the true elasticity is signi…cantly underestimated or that grandparental characteristics
matter beyond information incorporated in parental characteristics. We also …nd evidence
supporting the presence of a persistent dynastic component.
Preliminary draft
We thank Søren Leth-Petersen for helpful discussion.
Benjamin Ly Serena provided excellent research assistance. Financial support from WEST is gratefully acknowledged. Contact information: simon.h.boserup@econ.ku.dk, wojciech.kopczuk@columbia.edu, ctk@econ.ku.dk.
1
Introduction
The main objective of the literature studying intergenerational mobility is to analyze the extent to
which economic well-being is related across generations, and to try to understand the underlying
mechanisms (Piketty, 2000). In other words, the interest is both in the strength of the relationship
between lifetime economic resources/consumption possibilities of children and parents, and in
determining whether the statistical association is governed by mechanical transmission of abilities
and traits from parents to children or by active decision-making of parents, such as investment
in human capital of their children. Intergenerational correlations in earnings and income have
been extensively studied (see e.g. the surveys of Solon (1999) and Black and Devereux (2011)),
but much less evidence exists on intergenerational wealth mobility, even though wealth measured
at some point in life may be a proxy for lifetime economic resources that is as good as income
(or even better). An important exception is Charles and Hurst (2003), hereafter C&H, who
use wealth data from the Panel Study of Income Dynamics (PSID) to estimate the elasticity of
child wealth with respect to parental wealth for the United States. C&H obtain an age-adjusted
intergenerational wealth elasticity (IWE) of 0.37 before transfer of bequest (i.e., both parents
are alive), which is at the low end of the range of estimates of the intergenerational income
elasticity for the US, and …nd that around 2/3 of the elasticity is accounted for by income and
asset ownership.1
In this paper, we provide new empirical evidence on the intergenerational mobility of wealth
using Danish administrative wealth records of three generations observed for the entire Danish
population. Our data has several advantages. First, in our basic sample we have more than
1 million child-parents pairs compared to around 1500 in C&H. This allows us to include a
rich number of controls and to split the sample into age-cohorts while still obtaining very precise
estimates. Second, the use of administrative data removes problems of attrition and measurement
errors that often plague survey studies.2 Third, we are able to link comprehensive data for three
generations (child-parents-grandparents). The information about an additional generation allows
us to test whether child-parents relationships are stable and may also be used to address whether
1
Charles and Hurst (2003) review a few older studies looking at the intergenerational correlation of wealth.
These studies have looked at small non-representative samples with few observations and poor data quality.
2
Recent research has documented large survey measurement errors in key economic variables such as income
and that the errors are correlated with conventional covariates implying that errors are non-classical (Kreiner et
al., 2012).
1
the simple IWE estimate provides an accurate measure of the degree of persistence in the wealth
process across generations.
We contribute to the literature in a number of ways. We start by providing a theoretical framework capturing the relevant mechanisms that may create correlation of wealth across
generations and that lays the foundation for the empirical analysis. The standard Becker and
Tomes (1979, 1986) framework focuses on links in economic outcomes across generations due to
correlation of abilities across generations and due to parental investment in human capital of children. These channels determine the association of income across generations and therefore are
also likely to in‡uence the relationship between wealth across generations. In addition to these
mechanisms, however, wealth may be correlated across generations because of direct transfer of
wealth from previous generations (inter vivos or through inheritance), because of correlations
in patience and risk preferences creating di¤erences in saving propensities (Stiglitz, 1969), or
because of correlations in investment ability and the corresponding return (for example, due to
stock market participation, entrepreneurship, or attitudes toward borrowing). Individual wealth
observed at a given point in time therefore re‡ects in a complicated way economic resources,
abilities, and traits inherited from the previous generation, and we show theoretically how the
IWE coe¢ cient is related to these underlying mechanisms.
The …rst part of our empirical analysis follows C&H. We …nd an (unconditional) child-parent
age-adjusted wealth elasticity equal to 0.27 when focusing on indviduals with positive wealth as
they do. This estimate is considerably lower than the IWE estimate of C&H. When we address
the sample selection bias by using the full population, i.e., not removing child-parents pairs with
negative wealth of either child or parents (this is our baseline speci…cation), the estimate is even
lower at 0.19.3 Recent studies for France (Arrondel, 2009) and Denmark (Kolodziejczyk, 2011)
also …nd an IWE estimate of 0.2. The lower IWE estimate for Denmark is compatible with crosscountry studies of intergenerational earnings elasticities that …nd low elasticities in the Nordic
countries and the lowest elasticity for Denmark equal to 0.12 (Björklund and Jännti, 2009).
Life-cycle variation has proven to be an important consideration in the measurement of
3
C&H use a standard log transformation of the data and therefore remove non-positive values. However,
negative wealth may be optimal from an economic theory point of view in certain circumstances, in particular for
young individuals, and many individuals in our data have negative wealth. To allow for negative wealth, we apply
the inverse hyperbolic sine transformation (IHS) of the data, which yields identical results as the log transformation
for both positive wealth and the absolute value of negative wealth taken in isolation, but in addition allows for
parsimoniously combining the two.
2
intergenerational mobility in income that appears to be age-dependent (Haider and Solon, 2006).
Similarly, there may be substantial variation in the IWE depending on the age of the child and the
parents. To address this issue we run separate regressions for each age-cohort of the children and
for each age-cohort of the parents measured at the year when the child was born, respectively. The
IWE coe¢ cients are very precisely estimated and all lie within the range 0.16–0.22, revealing
a surprisingly stable relationship between child wealth and parental wealth. In our baseline
estimates, therefore, we can abstract from age-dependent di¤erences in wealth correlation and
proceed by pooling all cohorts while ‡exibly controlling for age of parents and children to adjust
for the life-cycle patterns.
We obtain a similar conclusion when introducing additional covariates and when splitting
the sample. When we add covariates that themselves have a strong explanatory power, such as
number of siblings dummies, income level, education length, and portfolio composition dummies,
the child-parents wealth elasticity falls but not by a lot. For example, income and education of
children and parents can only explain 8 percent of the original IWE estimate. The strongest e¤ect
comes from …nancial composition dummies that may explain 25 percent of the IWE, indicating
that correlation in household …nance behavior across generations may be important, but all
explanatory variables taken together can only explain up to 30 percent of the IWE. We also split
the sample according to parental age. This has quite a large impact on the estimates of the e¤ect
of child and parental income on child wealth, but only a small e¤ect on the IWE estimate.
Our theoretical framework suggests that robustness of our estimates to inclusion of income
and education (and to a lesser extent of …nancial composition dummies) is consistent with
parental wealth being a su¢ cient statistic for the mechanisms behind intergenerational correlation of wealth that these variables proxy for.
In the second part of our empirical analysis, we exploit availability of information about
grandparents. We start by addressing whether the relationship between child wealth and parental
wealth is stable over time/generations. Recent research has documented substantial changes over
the long run in top income shares, in the relative importance of capital and labor income at
the top of the income distribution, and in the evolution of inheritance (Atkinson, Piketty and
Saez, 2011; Piketty, 2011) and, similarly, there may be long run forces that reduce or increase
the strength of the relationship between wealth of children and wealth of parents. In light of
3
our theoretical framework, this would be so when parental wealth is not a su¢ cient statistic for
parental in‡uence, so that changing importance of di¤erent mechanisms behind intergenerational
correlation of wealth translates into changing the IWE. When estimating the intergenerational
elasticity of parental wealth with respect to grandparental wealth we obtain an estimate of the
IWE that is very similar to the estimate obtained from children-parents pairs. This is even more
striking when taking into consideration that the generations di¤er in many other respects than
just age, and indicates that the cumulative importance of the underlying mechanisms governing
the intergenerational relationship in wealth is quite stable.
Next, we look at the correlation between children and grandparents in isolation. If parental
wealth is a su¢ cient statistic for all previous generations then the coe¢ cient on grandparental
wealth should be the child-parents IWE raised to the power of two. We obtain a coe¢ cient
that is more than three times as high and very precisely estimated. This indicates that the
degree of persistence across generations is higher than what is re‡ected in the IWE estimate.
A reason may be that the underlying processes relating wealth across generations have longer
memory than just one generation, for example because grandparents have a direct impact on
their grandchildren (Solon, 2012). When including both parental and grandparental wealth in the
regression, we obtain a signi…cant and sizable coe¢ cient on grandparental wealth, while the childparents coe¢ cient only falls a little. This is consistent with the hypothesis of more persistence
and the underlying processes relating wealth across generations having longer memory than just
one generation.
Another likely reason for the signi…cant coe¢ cient on grandparents is measurement errors in
wealth or, in the same vein, that wealth is a noisy signal of abilities and traits transmitted across
generations and of the size of money transfers given from generation to generation. Attenuation
bias created by transitory components in the economic outcomes has been a major concern in
the intergenerational income mobility literature since the in‡uential contribution of Solon (1992),
and it is common to take averages over some years as we have done to reduce the importance of
transitory components. However, this method may only remove a small part of the attenuation
bias if the transitory component has some persistence (Mazumder, 2005) and would not work
at all to remove a bias from random "…xed e¤ects", e.g. you are born lucky in terms of ability
given your family background without transmitting this to your children. In the theory section,
4
we demonstrate how idiosyncratic variation in wealth may bias the IWE estimates downward,
but also discuss conditions under which it is appropriate to use wealth of grandparents as an
instrument for parental wealth in order to obtain consistent estimates. When we redo the …rst
part of the empirical analysis, we consistently obtain estimates of the IWE in the range 0.6-0.7,
which is more than three times as high as the original ordinary least squares estimates. This
points again to a much higher degree of persistence in the wealth formation across generations.
The exclusion restriction that allows for using grandparental wealth as an instrument for
parental wealth is strong. Hence, the results indicate one of the two possibilities: either IWE
is signi…cantly underestimated when using the conventional approach or the e¤ects extend for
more than just a single generation. In either case, we interpret it as indicating that the extent
of intergenerational mobility is substantially lower than a naïve estimate would indicate.
As an alternative approach, we further inquire into the degree of persistence by allowing for
dynasty …xed e¤ects. The standard Becker and Tomes framework, underlying intergenerational
empirical analyses, assumes that economic outcomes of all generations converge towards the same
constant. But as demonstrated by Stiglitz (1969) and in our theory section, people may belong to
di¤erent classes/dynasties who di¤er with respect to productivity or savings behavior, implying
that wealth, without any new shocks, converges towards a steady state distribution rather than
a constant. Our empirical analysis allowing for …xed e¤ects indicates that the model with a
common constant is misspeci…ed and therefore provides further evidence to the conclusion that
the conventional IWE estimates underestimate the degree of persistence.
The remaining part of the paper is organized as follows. Section 2 provides a theoretical
framework to understand the relevant mechanisms underlying the correlation of wealth across
generations and the challenges in estimating the degree of persistence across generations. Section
3 describes the construction of the data sets and provides summary statistics of key variables.
Section 4 describes the results of the empirical analysis. Finally, Section 5 o¤ers concluding
remarks and an appendix provides additional details concerning the data.
2
A theory of the correlation of wealth across generations
We start by providing a simple conceptual framework for understanding the relationship between
wealth of di¤erent generations. Let’s denote wg to be wealth of generation g. A member of
5
g
family i that belongs to generation g maximizes lifetime utility u(fCag ; qag ga=A
a=o ; "ig ), where Ca is
consumption at age a, where 0
a
A, qa are transfers to the subsequent generation made at
age a (inter vivos when a < A and bequests for a = A), and "ig is the set of taste parameters
characterizing preferences of this individual. Optimization is subject to the initial wealth of
W0g = 0 and the set of budget constraints for a > 0
Wag = Wag
1
(1 + rig +
a)
+ yag
Cag + Bag
qag ;
where Wa is wealth at age of a, yag is income at the age of a, Bag is the bequest received from
the previous generation at age of a (with one member per generation, Bag = qa~g
1
where a
~
a is
the age di¤erence between the parent and the child), rig is the mean rate of return speci…c to
that particular individual (to allow for varying investment strategies), and
a
is the mean-zero
deviation from the normal rate of return. Consequently, the level of wealth can be expressed in
terms of the exogenous parameters of the problem as
Wag fqbg
1 A
a
gb=0 ; fybg gA
b=0 ; rig ; "ig ; f b gb=0
:
(1)
In other words, wealth at any given age depends on the history and future (expected) transfers
from parents, the history and future own income, the rate of return, preference parameters, and
stochastic shocks.
We are interested in understanding the relationship between wealth of members of di¤erent
generations. Most simply, one can observe the statistical association that may be, for example,
described using the correlation coe¢ cient corr(Wag ; Wa~g
1
), where a and a
~ are ages at which we
observe wealth of children and parents, respectively, or the empirical association between some
transformation of observed wealth levels
d wag
,
d wa~g 1
where (if we focus on positive wealth) we could
use for example w = ln(W ) or (as we will do in what follows) we can use the inverse hyperbolic
p
sine transformation w = log(W + W 2 + 1) that behaves as log(jW j) everywhere with the
exception of in the neighborhood of zero.
Let’s focus attention on
d wag
d wa~g
1;
which we will refer to as the intergenerational wealth elasticity (IWE). Wealth of parents does
not enter directly as an argument of child’s wealth (Equation (1)), but rather it may be either
6
correlated or causally related to the other arguments. Hence, it should be intuitive that this is
not a well-speci…ed concept, without taking a stand on why wa~g
1
varies. By investigating the
determinants of wealth in Equation (1), one can identify a number of reasons why wealth could
co-vary:
transfers from parents qbg
1
are a function of their own characteristics and hence correlated
with parental wealth
incomes of parents and children may be correlated for many reasons extensively analyzed
in the literature
rates of return and preferences may be correlated across generations
Depending on the relative importance of these factors, we may expect to see di¤erent relationships at di¤erent times and places and di¤erent sample choices unless they happen to correspond
to precisely the same strength of correlation in wealth. We expand on and formalize this intuition
in what follows.
In order to make progress and introduce our empirical speci…cation, we simplify our framework to resemble what has been sometimes dubbed the “mechanical” approach in the literature
(Goldberger, 1989). It amounts to positing a statistical relationship between variables of di¤erent
generations without explicitly specifying the nature of the individual optimization problem. We
adopt this terminology but note that the framework we described is an optimization framework,
except that we have refrained so far from imposing additional assumptions so that the framework
serves only to identify the relevant variables. Our main simpli…cation in what follows is approximation of the (potentially nonlinear) relationship rather than assuming away optimization.
In order to operationalize our empirical approach, we linearize our original wealth formula as
wag
where
+
g 1
q qa
+
g
y ya
+
r (1
+ rig ) +
" "ig
+
g
a;
(2)
is an error term incorporating rate of return shocks and approximation errors that is
assumed (very strongly) orthogonal to the other variables and we posit that the current values
of right hand side variables are su¢ cient to summarize the relationship with wealth. While we
write all terms in a linear fashion to simplify notation, they can correspond to transformations
(e.g., log or IHS) of the original variables.
7
When we estimate the statistical relationship between wag and wag
wag =
the coe¢ cient
w
g 1
w wa
1
as
+ !;
(3)
is going to re‡ect the average impact of wag
1
running through all four possible
channels: bequests, income, preferences, and rate of return. Our objective in the rest of this
section is to clarify the interpretation and estimation of
w.
In what follows, we abstract from the age aspect of inter-generational relationship (we will
return to considering it in the empirical work). It will prove useful to write the determinants of
wealth as a vector xg = (q g
1; yg ; 1
+ rig ; "ig ;
g ),
with wealth expressed as
wg = x g +
where
g
g;
is white noise measurement error. Finally, we specify the law of motion for determinants
of wealth as
xg = xg
1
+
g
:
(4)
We assume for now that it is autoregressive of order one, but deviations from this assumption
will be important to consider in what follows. Equation (4) describes the relationship between
characteristics of subsequent generations other than wealth. In what follows we will consider a
special case when the relationship between xg
imposes structure on matrix
1
and xg runs through wealth — that special case
but otherwise yields the law of motion (4).
Note that we have introduced many potentially unobservable sources of variation in wealth.
First, taste parameters " are likely unobservable directly (though perhaps they may be proxied
for). It is natural to consider and test whether correlation in preferences is a source of intergenerational persistence. Second, we split the rate of return into two separate components. One
is the normal rate of return — this is akin to a preference parameter in the sense of re‡ecting
traits of individuals that lead them to select investments with varying outcome, although it is
conceptually distinct since it represents manifestation of preferences through choices rather than
preferences themselves. The other one is
that corresponds to deviations from the normal rate of
returns (and approximation errors that we abstract from). We assume that it is an idiosyncratic
components so that
is assumed not to be correlated across generations (
= 0). We include
it though in xg , because it is certainly possible that such random shocks to wealth do in fact
8
have an impact on the subsequent generations by in‡uencing other variables. The …nal source
of randomness is
— this is assumed to be measurement error or other sources of variation in
wealth that have no consequence for the subsequent generations.
Using this notation (and expressing all variables in terms of their deviation from the mean
in order to eliminate the constant term), we can re-write wealth as follows:
wg = x g +
where
and
g
w
g
= xg
+
1
+
g
g
=
w xg 1
+
g
=
w wg 1
is a linear projection (linear regression coe¢ cient) of xg
is the corresponding residual. In other words,
w
w g 1
+
+
g
+
1
g
g
(5)
on xg
1
summarizes the statistical relationship
between wealth of the two generations that runs through the set of characteristics in x (with
orthogonal noise terms excluded).
More explicitly, using the standard OLS formula (X 0 X)
xg
1
value of
+
g
w
+
g
and noting that
+
g
1X 0Y
is orthogonal to xg
1
with X = xg
1
and Y =
, we can write the expected
as
E[
j xg ; xg
w
1]
=
= (
showing how
w
(xg
1
0
(x0g
)0 xg
1
1
1 xg 1 )
)
(xg
1
)0 (xg
1
0
(x0g
1
1 xg 1 )
)
;
(6)
summarizes the complicated web of in‡uences that links wealth across gener-
ations. It re‡ects the causal relationship between relevant arguments of Equation (2) ( ) that
can be mapped to one-dimensional wealth within each generation via . In general, the mapping
of wealth across generations depends on the distribution of characteristics in the population x.
This is because there are many channels through which characteristics of subsequent generations
relate, and the population relationship between wealth of di¤erent generations re‡ects di¤erent
components of
presence of x0g
depending on variation of xg
1 xg 1
The coe¢ cient
1
in the population. This is re‡ected by the
in the equation.
w
is as close as one can get to a “structural” intergenerational correlation
of wealth if one insists on summarizing it by a single parameter. In the special case where xg
is one dimensional, so that
w -coe¢
is a scalar, it is easy to show that
cient reveals the (single) structural parameter.
9
w
=
1
, implying that the
2.1
Interpretation of
More generally,
w
w
is a relationship that is speci…c to a given population and it does not have
a direct causal interpretation. This is because the source of variation in wealth (wg
depending on which component of xg
1
1)
matters:
is responsible, the e¤ect will vary accordingly.
w
does
though re‡ect the e¤ect of variation in wealth in the population that combines in‡uences from
a variety of sources.
To illustrate the logic of this formula, consider the following example
Example 1 Suppose that elements of x are uncorrelated with each other (x0g xg is diagonal),
is diagonal and only two elements of
, indexed by i and j are non-zero. Then straightforward
manipulation yields
w
where
2
ii
=
2 2
i ii ii +
2 2
i ii +
2
j
2
j
2
jj jj
;
2
jj
is the (i; i) element of x0g xg (variance of ith element of xg , denoted by xgi ) and
the (i; i) element of
ii
is
.
In this particular example, the correlation of wealth has its source in two di¤erent channels,
i and j. A marginal increase in xg
g
1 (wg
1)
and into a
i ii
1;i ,
translates into a
increase in wealth of generation
increase in wealth of generation wg . Hence, the intergenerational
elasticity driven by this source of variation is
driven by the jth element is
i
jj .
ii .
Analogously, the intergenerational elasticity
When both of the sources are present at the same time,
w
has to re‡ect both of these sources and their contribution depend on the relative magnitudes
of
2 2
k kk
(k = i; j). This is intuitive: what matters is the extent to which a given channel is
responsible for variation in wealth — this is a¤ected by the extent to which the given channel
in‡uences wealth (
k)
and the extent of variation in the underlying characteristics,
Note that even when one is willing to assume that
and
kk .
are structural parameters, there
is no single structural intergenerational elasticity here. Di¤erent societies at di¤erent points in
time may di¤er with respect to the extent of variation in determinants of wealth — variation
in bequests, tastes, education, rate of returns may all vary over time with institutions, policies,
culture, etc. Each of such situations will correspond to a di¤erent weighted average of
jj
and as will the measured IWE.
10
ii
and
Another way of phrasing it is that the intergenerational wealth elasticity is the average
treatment e¤ect corresponding to changes in wealth of the prior generation. Since prior wealth
may be varying for a multitude of reasons (corresponding to di¤erent impacts of the treatment
— change in prior wealth), the corresponding estimate will re‡ect a weighed average impact with
the weights being sample-dependent.
The example is of course restrictive, but illustrative of the logic of Equation (6) that characterizes the general case.
In the special case when
ii
=
jj
the source of variation does not matter because the
intergenerational elasticity stemming from the two di¤erent sources happens to be the same. A
priori, this does not seem likely, but we next discuss a more general case where independence of
the source of variation can stem from a less arbitrary assumption.
2.2
Parental wealth as a su¢ cient statistic
As discussed above, in general there is no single intergenerational elasticity of wealth because
di¤erent sources of variation in parental characteristics may in general translate into di¤erent
strengths of intergenerational association. However, it is possible to identify a special case when
it is not so. Imagine that parental wealth is a su¢ cient statistic for the e¤ect of parental
characteristics on wealth of children. That is, retaining the linear structure, suppose that
xg = (wg
for some vector
1
g 1)
= wg
1
g 1
(and note that we are using observed wealth net of
term). Then, xg = xg
— the measurement error
, so that — using our general notation —
1
=
and
=
.
Substituting into Equation (6) yields
E[
w
j xg ; xg
1]
=(
0
(x0g
1 xg 1 )
)
which can also be seen directly from wg = xg +
1
g
0
= wg
(x0g
1
1 xg 1 )
+
g
=
g 1
;
.
When parental wealth is a su¢ cient statistic for the characteristics of parents, the IWE is
equal to
of xg
regardless of the source of variation in wealth — the formula for E[
1.
11
w]
is independent
2.3
Testing the importance of di¤erent channels
So far, we have clari…ed the theoretical relationship between wealth of di¤erent generations
while allowing for many di¤erent channels of interactions. Consider now the possibility of directly
observing some of them. Speci…cally, suppose that we partition x = (x1 ; x2 ) with x1 unobservable
and x2 observed. Similarly, let’s denote by
x1 : x1g = x1g
1 11
+ x2g
1 12
wg = x g +
1
w
where
and
x2g
=
1
w xg 1
=
1
w wg 1
g
1.
g
+
= x1g + x2g +
+ x2g
+ x2g
(with
and
2
w;g
and
12
the partitions of matrix
that determine
Then,
2
1 w;g 1
2
1 w;g 1
is a linear projection of x1g
2
w;g 1
11
g
= x1g
+ x2g
2
w;g
1 11
+
+ x2g
+ x2g +
1 12
1
g
+
g
1
+ x2g
2
w;g
1
w g 1
1 11
on xg
1
+
1
;
(7)
while partialling out the e¤ect of x2g
1
being the resulting coe¢ cients). In other words, by controlling for
some subset of characteristics of both parents and children (note that controlling for both at the
same time is important), we can zoom in on the e¤ect of the remaining characteristics that is
orthogonal to the observed ones.
2.4
Measurement error
Simple inspection of relationships (5) or (7) reveals that OLS of wg on wg
estimate
that wg
w
1
=
1
w ).
(or
xg
1
This is because the error term
+
g 1
g 1
1
will not in general
will be correlated with wg
1
— recall
or, more explicitly, the relationship is described by Equation (2).
The attenuation bias due to the presence of
will not be a problem only when var( ) = 0. One
may of course make assumptions to that e¤ect, but absent these assumptions, our estimate of
w
will be biased.
Assuming that the measurement error term
of preceding generation xg
instrument to consider is wg
2
g 1
is not serially correlated, characteristics
can serve as an instrument for wg
2.
1.
In particular, a natural
Under the simple autoregressive structure of order one that we
assumed, the exclusion restriction is satis…ed and this is a valid instrument.
Similarly, speci…c components of xg
2
could be used as instruments. Note though that
di¤erent instruments will identify di¤erent average treatment e¤ects, i.e., in our case they will
identify the weighted average of e¤ects going through the channels that the instrument covaries
12
with.
2.5
Multiple generations
We also have assumed so far that the characteristics follow the simple autoregressive structure
of order one. Two natural generalizations are to consider a higher order autoregressive structure
and to consider a …xed (or very persistent) family component.
Suppose …rst that xg follows a second-order autoregressive process, xg = xg
while we continue to have wg = xg +
y
=[
1;
yg ,
y,
y
2]
so that yg = yg
1
y+
throughout in place of xg ,
g
g.
We can de…ne yg = (xg ; xg
and wg = yg
and
y
+
g
where
y
1 ),
= ( ; 0;
yg
1
1 +x
1
= (xg
g 2
2+
g,
1 ; xg 2 ),
; 0). Substituting
allows for repeating the whole argument, but now
with the set of characteristics expanded to include grandparental ones. On the conceptual level,
grandparental characteristics become yet another determinant of IWE.
In the presence of a family …xed e¤ect, we can analogously expand the de…nition of xg to
include the constant family term.
While both of these extensions are straightforward for the purpose of understanding the
IWE
w,
they raise additional estimation issues. First, they invalidate the possibility of using
grandparental characteristics as an instrument. Second, eliminating the …xed family component
in order to understand the importance of this channel is complicated due to the presence of
lagged dependent variable structure.
2.6
Empirical strategy
We will proceed as follows. First, we will estimate population
w.
We will follow it by considering
various subsamples and di¤erent generations in order to test the robustness of this estimate.
Sensitivity of the results to di¤erent sample choices would indicate that the relative importance
of di¤erent channels varies depending on the subsample. Lack of sensitivity would indicate
either that wealth is a su¢ cient statistic or that, in fact, di¤erent samples considered happen to
correspond to a similar mix of channels behind intergenerational correlation of wealth.
Next, we will consider controlling for di¤erent channels by including the corresponding characteristics of parents and children, and investigating the sensitivity of IWE to these choices.
As we discussed, this approach allows for shedding light on whether the e¤ect of the particular
channel can be summarized through its impact on wealth.
13
Finally, we will consider grandparental characteristics to investigate the relevance of interactions that run across multiple generations.
3
Data
Our empirical analysis is based on data from several public administrative registers gathered
by Statistics Denmark and linked together using personal identi…cation numbers. Every citizen
in Denmark is assigned a unique personal identi…cation number at birth and the identi…cation
numbers of the mother and the father are registered for all Danes born in 1960 and onwards.4
This enables us to combine di¤erent data sources at the individual level and to link data across
generations.
The data on individual wealth and income is based on administrative tax return records,
rather than survey questions as in Charles and Hurst (2003) and most other studies on intergenerational mobility. The Danish Tax Agency (SKAT) collects, in addition to information of
various income sources, information about the values of asset holdings and liabilities measured
at the last day of the year for all Danes, and the bulk of the wealth components are third-party
reported.5 The available pieces of information at Statistics Denmark are the aggregate value of
assets and liabilities, respectively, covering the period 1980 to 2011, and from 1997 and onwards
it is also possible to obtain complete portfolio information with respect to the value of bonds,
stocks, cash in banks, house, mortgage loans and sum of other loans. Another attractive feature
of the wealth data is that the information is not top coded.
The information about the value of …nancial assets and liabilities at the end of the year
is reported to the tax authorities by banks, other …nancial institutions, and some government
institutions, while the cash value of property is assessed by the tax authorities, based on detailed
information of the property, and used for taxation of the imputed rent on the property. The
third-party reported value of assets includes all deposits, stocks, bonds, value of property, and
4
Registrations of parents exist before 1960 but are incomplete.
The tax authorities use the income information to generate pre-populated tax returns. The information on
wealth was originally used to compute the wealth tax, whereas today it is used by the tax agency to cross check if the
reported income level is consistent with the change in net-wealth during the year under the assumption of a given
estimated consumption level. A recent study by Kleven et al. (2011) reveals, using a large scale randomized tax
auditing experiment constructed in collaboration with the Danish tax authorities, only small di¤erences between
the third-party reported income items and the corresponding items on the …nal tax return. This indicates that
the third party reported information of the Danish Tax Agency is of a very high quality.
5
14
deposited mortgages. Pension funds are not included. The third-party reported value of liabilities
includes debt in …nancial institutions, mortgage credit debt, credit and debit card debt, deposited
mortgage debt, student debt and debt in The Mortgage Bank (a public institution), debt to
…nancial corporations, debt to the Danish municipalities and other liabilities such as unpaid
taxes and mortgage debt, which are not deposited.
From 1980 to 1996, Denmark had a wealth tax, and taxpayers had to self-report car values,
boat values, caravan values, title deed of cooperative dwellings, premium bonds, cash deposits,
stocks (both listed and non-listed thereby including privately held companies), and private debt.
These components are not included in the computations after 1996. Until 1996 the value of
stocks was self-reported, while afterwards it became third-party reported by banks and …nancial
institutions (excluding non-listed stocks). The registration of the company value of self-employed
has changed several times, but has stayed unchanged since 1997, where assets and liabilities of
the …rm were registered separately and included, respectively, in the assets and liabilities of the
owner. Another de…nitional change occurs in 1983. Before 1983 all family wealth of a married
couples was assigned to the husband, while the wealth of husbands and wives has been registered
separately afterwards.
Ideally we would like to observe wealth, income, etc., of the individual in the middle age and
observe the di¤erent generations at the same age because of the life-cycle variation in economic
outcomes (Haider and Solon, 2006). If, for example, parents are around 25 years old when their
children are born and we observe wealth of the child generation in 2011, then we would like to
observe wealth of the parents and grandparents in 1986 and 1961, respectively. This goal has
to be balanced against data availability (grandparents) and data quality (parents). Our main
empirical analyses are based on parental wealth observed in 1997-1999, where the de…nition
of the wealth measure is the same as that used for children in 2009-2011, and grandparental
wealth measured in 1983-1985 where wealth of biological grandfathers and grandmothers are
more accurately measured than the years before. We take three year averages of wealth of each
individual to reduce the importance of transitory components, as often done in the literature
following Solon (1992). The e¤ects on our estimates of this procedure are rather small.
The largest change in the de…nition of wealth occurs around 1997 where the wealth tax was
abolished. However, for 1995 and 1996 Statistics Denmark computed assets and liabilities of
15
each individual using both the new de…nition of wealth (used for children and parents) and the
old de…nition (used for grandparents). In Appendix A, we exploit this overlap to show that the
new wealth measure is well approximated by the old way of measuring wealth, and we provide
more details on the wealth data. Additional information on the Danish wealth and income-tax
data may be found in Leth-Petersen (2010) and Chetty et al. (2011).
In the empirical analysis, we consider two types of samples: a child-parents sample (CP)
and a child-parents-grandparents (CPG) sample. The CP sample focuses only on child-parents
relationships without exploiting information of grandparents. In this sample, we consider all
children of age 21-51 in 2011 (ensuring that they are born in 1960 or later), where both parents
are alive in 2011, and where both parents are between 21 and 66 years old in 1999. This is very
similar to Charles and Hurst (2003) with the exception that they limit the sample to children
that are older than 25 years and require that both children and parents have positive wealth.
The importance of these two di¤erences in sample selection will be discussed. The child-parentsgrandparents (CPG) sample is based on the CP sample, but with the additional requirement
that at least one grandparent is alive in 1985. To avoid selection problems, we further require
that parents are born in 1960 or later, corresponding to a maximum age of 39 in 1999, implying
that the personal identi…ers of all the grandparents are known.6
Table 1 provides summary statistics of the two samples. In the CP sample, we have 1.16
million child-parent pairs and the CPG sample consists of 97 thousand observations. In both
samples, parents are signi…cantly older than their children at the time where wealth levels are observed in the data, and grandparents are older than parents in the CPG sample. Since households
normally accumulate wealth over the life cycle up to retirement, we should expect to observe
the highest wealth for grandparents and higher wealth for parents than for children, which is
also the pattern we see in Table 1. The large sample sizes allow us to account for the life-cycle
e¤ects by age-adjusting the wealth levels using age dummies and to estimate separate e¤ects for
di¤erent child cohort–parent age constellations in the empirical analyses. Moreover, following the
existing literature measuring intergenerational e¤ects, we will relate relative di¤erences within a
generation to the relative di¤erence of another generation, which is not sensitive to scale e¤ects.
Notice that wealth is negative for many individuals. This is in particular the case among the
6
This reduces the sample considerably. Without the restriction, we obtain the same regression coe¢ cients and
a higher statistical precision but we prefer the restricted sample to avoid sample selection bias.
16
child generation where around half of the individuals have negative wealth compared to eight
percent in the sample of C&H. One reason is that we do not restrict the sample to children above
25 as C&H, which signi…cantly increases the wealth of children but also of parents, who will on
average be older. Another reason is that Danish households have very high debt-to-income ratios
(the liability-gross income ratio is around 200 percent for children and 150 percent for parents in
the CP sample) compared to other countries, which has received international attention recently
(IMF, 2012; European Commission, 2012). The di¤erence to the US and other countries probably
re‡ects that Denmark has a reasonably high universal public pension bene…t level, substantial
labor market pension savings by international standards, and an extensive social safety net that
reduces the need for precautionary savings.
Labor earnings and gross income are on average higher for parents than for children, while
earnings for grandparents are lower than for parents re‡ecting that some of the individuals have
retired. The table also reports the years of education counting completed education. Parents are
clearly more educated than grandparents but also somewhat more educated than their children
in the CPG sample. However, this re‡ects that many of the children have not yet completed
their education.
4
Empirical analysis
4.1
Elasticity of child wealth with respect to parental wealth
We …rst use the child-parents (CP) sample described above to estimate the (unconditional)
elasticity of child wealth with respect to the average wealth of the (biological) parents.7 This
corresponds to estimating an ordinary least squares regression after using the natural log transformation on the wealth measures of children and parents. Column 1 of Table 2 reports the
estimated elasticity without age adjustment, while column 2 reports the age-adjusted elasticity
obtained by including age dummies of both children and parents in the regression. The …nding
of a child-parents age-adjusted elasticity equal to 0.268 implies that children born of parents
with a wealth level that is 10 percent above the mean of the parent generation can expect to
obtain a wealth level that is 2.7 percent above the mean of the child generation. C&H obtained
an age-adjusted intergenerational wealth elasticity (IWE) of 0.365 for the United States using
7
Results are unchanged if we use the aggregate wealth of parents instead of the average wealth of parents, which
is due to the fact that the log transformation and the IHS transformation of the data remove any scale e¤ects.
17
the PSID survey data. The lower estimate for Denmark is not surprising. Denmark has a very
homogeneous population and a high degree of redistribution, and comparative studies have found
that Denmark has the lowest intergenerational elasticity of earnings/income.8
When applying the log transformation, we are throwing away all child-parents pairs where
either the child or the parents have zero or negative net wealth. Most of the empirical literature
analyzing intergenerational relationships have looked at economic outcomes that do not attain
negative values by de…nition, for example earnings. In this case, it is natural to apply the log
transformation, which has appealing properties. This is, however, not the case when analyzing
net wealth, which may well be negative, and where standard life cycle theory predicts negative
values for young persons who have increasing earnings pro…les. Another reason for observing
negative wealth of households in our case, and also in C&H, is that we are unable to include
pension wealth. In order to avoid the potential selection problem of using the log transformation,
we will for the remaining part of the paper be using the inverse hyperbolic sine transformation
p
(IHS), w = log(W + W 2 + 1), that behaves as log(jW j) everywhere with the exception of in
the neighborhood of zero.9 Column 3 shows the IWE estimate after using the IHS transformation
on the sample where wealth is restricted to be positive. The estimate is completely identical to
the result based on the log transformation in column 2. Next, we consider the full sample with
1.16 million child-parents observations that include negative wealth of children and/or parents.
This gives an IWE of 0.19, which is considerably lower than the estimate obtained from the
restricted sample, showing that it may create severe selection bias to remove observations with
negative wealth. Note …nally from Table 2 that all regression coe¢ cients are very precisely
estimated because of the large sample size as illustrated by the tiny standard deviations of the
estimates.10
Life-cycle variation may be important when measuring intergenerational mobility in economic
outcomes (Haider and Solon; 2006). Thus, there may be substantial variation in the IWE,
depending on the age of the child and the parents, that are not removed by including age
8
An overview of estimates of intergenerational earnings elasticities for di¤erent countries may be found in
Björklund and Jännti (2009). They report an elasticity for Denmark of 0.12, which makes Denmark the country
with the lowest correlation across generations.
9
For details on why the IHS transformation can be used to estimate approximate elasticities, see Appendix B.
10
Another concern may be that outliers or observations with zero or close to zero wealth may be very important
for the estimates. We have run sensitivity analyses, which revealed no e¤ects on the estimates of removing
observations in the tale of the distribution and around zero wealth.
18
dummies. The large sample size allows to address this issue by running separate regressions for
each age-cohort of the children and for each age-cohort of the parents measured at the year where
the child was born, respectively. Figure 1a shows the IWE estimate as a function of the age of
the child in 2011 starting from the early twenties and going up to an age of …fty years. The
diagram is constructed by running separate regressions for each cohort of the children, including
in each regression age dummies of the parents, and then plotting the estimates and the 95 percent
con…dence interval for each cohort. The con…dence interval shows that the IWE is very precisely
estimated for each age group and the graph displays a remarkably stable IWE. For all thirty age
groups, estimates lie within a narrow interval from 0.16 to 0.22 without any systematic trend.
Figure 1b is constructed in the same way but this time subsamples are created for each age
level of the parents at the time when the child was born and child age dummies are included
in each regression. The graph shows a weakly increasing correlation of wealth between children
and parents when the age-di¤erence between parents and children is increased, but the main
conclusion is again that the IWE is remarkably stable and within the same interval as in Figure
1a.11
4.2
Decomposition of the intergenerational wealth elasticity
In Table 3, we add income controls. Column 1 is the baseline without income controls and is
identical to column 4 in Table 2. We …rst include the income of the child. It is natural to expect
that a high income level of the child is associated with a high level of wealth. This is also what
we see from column 2 showing that the elasticity of child wealth with respect to child income
equals 1.4, implying that a ten percent higher income level is associated with 14 percent higher
wealth. Our main interest is how it in‡uences the size of the IWE. If parents with high wealth
invest more in the human capital formation of their children, as in the theory of Becker and
Tomes (1979) then this would raise the income and wealth of their children. This would generate
a positive correlation between child wealth and parental wealth working through child income,
and if this channel was stronger than other sources of intergenerational correlation in wealth,
the IWE estimate should fall when we introduce child income as a regressor. Table 2 shows that
the IWE is unchanged after introducing child income, and does therefore not lend support to a
11
We have also estimated the IWE for each child-parent age constellations. All estimates are signi…cant with
the exception of constellations where the age-di¤erence between the child and the parents is very small or very
large. The conclusion is again that estimates are roughly the same for all combinations.
19
mechanism working through child income.
Next, we also introduce parental income in the OLS regression. Column 2 shows that the
elasticity of child wealth with respect to parental income is 2.2, which is therefore more important
than the child’s own income. This corresponds closely to the speci…cations we discussed in our
theoretical section: the objective is to shut down income as a mechanism of intergenerational
transmission of wealth, and it requires controlling for income of both parents and children.
It could be that parental wealth was not directly relevant for wealth of children, but own
income was an important determinant of own wealth. If it was so, correlation of income would
translate into unconditional correlation of wealth. Unconditional correlation between wealth of
children and parents could also arise if the true relationship was from parental income to child
wealth, because parental wealth works as a proxy for parental income.
In each of these cases, the IWE would fall when controlling for parental income, but we
observe nearly the same estimate as in column 2. Altogether, the IWE falls only slightly when
going from column 1 to column 3. Income explains less than 8 percent of the IWE, and this
conclusion is completely unchanged if we use a more ‡exible speci…cation with, for example,
fourth degree polynomials in child income and parental income, respectively.
The last two columns, report the result of splitting the sample depending on parental age.
This has a sizable impact on the coe¢ cients on income but only a small impact on the IWE.
Note that the coe¢ cient on the child’s own income becomes negative. This may re‡ect that the
children are young in this group and that students, who currently have a low income (student
bene…ts), come from a wealthy background and are wealthy themselves compared to young
persons earning income in the labor market.
In Table 4, we include number of siblings dummies, years of schooling dummies, and …nancial
composition dummies. The idea here is to test the independent importance of the corresponding
mechanisms beyond their relationship to wealth.
Column 1 is the baseline with only age dummies included. In column 2, we include number of
siblings dummies, so that we only exploit the variation within families of a given size to estimate
the IWE. It is certainly possible that the number of siblings might a¤ect one’s own wealth
separately from any relationship that it might have with parental wealth. For example, siblings
may reduce incentive to save if they provide an implicit insurance or the number of siblings
20
may in‡uence traits that are determinants of wealth accumulation such as patience. Inclusion
of sibling dummies has nearly no impact on the estimate suggesting that sibling considerations,
if any, are adequately captured by parental wealth. Similarly, dummies for education length of
both parents and children reduce the IWE only a little, and the e¤ect is of the same magnitude
as when introducing income controls (see column 3 of Table 3), suggesting that wealth is also a
good proxy for this channel.
The largest reduction in the IWE arises when we introduce …nancial composition dummies
for children and parents, i.e., dummies for homeownership, stock ownership, bonds ownership,
and for being self-employed. This reduces the IWE by 25 percent, which is much more than what
is explained by the income controls alone. Finally, when including all control variables the IWE
becomes 0.134, which is a reduction of the IWE by less than 30 percent when starting from the
baseline with only age controls. Thus, the explanatory variables explain only up to 30 percent
of the IWE, which is considerably less than in C&H where income alone explains more than 50
percent of the IWE, and all variables together explain nearly 2/3 of the IWE.
4.3
Wealth across three generations
In this subsection, we use the child-parents-grandparents (CPG) sample, which enables us to
analyse wealth across three generations. The children and parents are younger in the CPG
subsample than in the full CP sample. For comparison, we therefore start by running a simple
regression of child wealth with respect to parental wealth for this subsample. The result is
reported in column 1 of Table 5 and gives an age-adjusted elasticity of 0.177, which is only a
little smaller than the elasticity obtained when estimating the relationship on the full sample
(column 4 of Table 2).
It is important to know whether the relationship between child wealth and parental wealth is
stable over time/generations. There may be long run forces that reduce or increase the strength
of the relationship, and recent research has documented substantial changes over the long run in
top income shares, in the relative importance of capital and labor income at the top of the income
distribution, and in the evolution of inheritance (Atkinson, Piketty and Saez, 2011; Piketty, 2011).
In column 2, we report the relationship between parental wealth and grandparental wealth in the
data set. The age-adjusted child-parents wealth elasticity from this estimation is 0:160, which is
only slightly lower than the IWE when running the regression on the child-parents pairs in the
21
sample, and the standard deviations on the estimates from these two regressions are small and
completely identical. This indicates that the underlying intergenerational relationship is quite
stable.
Next, we look separately at the correlation between children and grandparents. From a
structural relationship only relating generation g to generation g 1 such as wg =
we would expect that a regression of wg on wg
2
0 + 1 wg 1 +",
would give a coe¢ cient equal to (
2
1) .
From
the IWE estimates in columns 1 and 2, we should therefore expect a coe¢ cient around 0:03 (i.e.,
0:1772 = 0:031 and 0:1602 = 0:026). The estimated coe¢ cient we obtain from regressing child
wealth on grandparental wealth is 0:094 (column 3 of Table 5) and is therefore more than three
times as large. One reason for this di¤erence could be that the underlying stochastic processes
relating wealth across generations have more memory than just one generation, for example
because grandparents have a direct impact on their grandchildren (Solon, 2012). Another possible
reason, which we pursue in the next subsection, is measurement error/omitted variable that
creates a downward bias in the estimated coe¢ cient.12
Column 4 of Table 5 reports the results from including both parental wealth and grandparental wealth in the estimation. When compared to the univariate relationships (columns 1
and 2), we see that the coe¢ cient on parents fall a little, whereas the coe¢ cient on grandparents
falls by 1/3. If we consider a ten percent increase in the wealth of grandparents then this regression predicts a nearly one percent higher wealth of the grandchildren, which is again three times
as high as the prediction we obtain from a standard estimation of IWE exploiting data from
only two generations. In Table 6, we add the same controls as we did in Table 4 plus dummy
variables for number of cousins and for number of living grandparents in 2011.13 Introducing the
demography variables in isolation reduces the coe¢ cients on parents and grandparents a little
(going from column 1 to column 2). The e¤ects on the coe¢ cients are larger when including
education and …nancial composition dummies (column 3), as was also the case when we looked
12
If, for example, only 50 percent of the measured variation in wealth is governed by the true variation while
the rest is noise then we would estimate a 1 coe¢ cient around 0:2, when the structural coe¢ cient is 0.4. The
true coe¢ cient on grandparents would be 0:4^2 = 0; 16, but we would estimate 0:16 50% = 0:08, which is higher
than 0:2^2 = 0:04.
13
If grandparents transfer money to grandchildren then the e¤ect of many cousins would be less money received
on average per grandchild. By including dummy variables for number of cousins, we are only exploiting the
variation within families of same size (measured by the number of cousins). We include dummy variables for
number of living grandparents in 2011 because grandparents may die after we have observed their wealth in
1983-85, implying that parents and children may inherit their wealth.
22
at the relationship across only two generations in Table 4. The e¤ect of grandparental wealth on
child wealth is again three times as big as the predicted e¤ect from a standard two-generation
estimation of the IWE.
4.4
Using grandparental wealth as instrument
Attenuation bias caused my measurement problems has been a main issue in the intergenerational income mobility literature since the in‡uential contribution by Solon (1992). Measurement
problems may for example be caused by response errors in surveys and by transitory components
in income implying that current income is a pure measure of the permanent income. The standard method to reduce the in‡uence of the transitory component is to compute three or …ve year
averages, as we have also done in our measurement of wealth. However, this method may only
remove a small part of the attenuation bias if the transitory component has some persistence.
For example, Mazumder (2005) provides simulations suggesting that it may require an average
over 20 to 30 years in order to bring the attenuation factor down to 90 percent.
The theory in Section 2 illustrates cases where child wealth only depends on parental wealth
and where ordinary least squares estimation of the relationship provides a downward biased
estimate of the IWE, but where two-stage least squares estimation using wealth of grandparents
as instrument for wealth of parents provides a consistent estimator. Table 7 reports results from
such 2SLS estimations. The two …rst columns report 1st stage and 2nd stage results with only
age dummies as additional regressors, while the following columns report results when other
variables are added. The strong correlation of parental wealth with grandparental wealth and
F-test values well above 10 in all cases indicate that we do not have a ‘weak instrument’problem
in the 1st stage regressions.14 The 2nd stage results give estimates of the IWE in the range
0.6-0.7, which is more than three times as high as the ordinary least squares estimates described
in Subsection 4.1. For robustness, we have redone the age-dependency graphs in Figure 1a and
1b, but this time displaying the 2SLS estimates. This is done in Figure 2a and 2b, which for
14
As a further test of the strength of the …rst stage, we have constructed a worst case scenario where grandparental wealth has no predictive power for parental wealth following the approach of Bound, Jaeger, and Baker
(1995). We achieve this by randomly assigning the observations of grandparental wealth to the observations in
data. The resulting pseudo instrument is by construction uncorrelated with the endogenous regressor, yet, it
retains the marginal distribution of the actual instrumental variable. Using the pseudo-instrument gives an IV
estimate close to the OLS estimate, and standard errors are much higher compared to the actual IV standard
errors.
23
comparison also include the OLS estimates of Figure 1a and 1b. The graphs based on the 2SLS
estimates have the same shapes as the graphs based on the OLS estimates, but of course with
a more wide con…dence interval. More importantly, the IWE estimates are consistently around
three times as high at each age level.
4.5
Dynasty …xed e¤ects
In Section 2, we also consider the possibility of a dynasty/social class …xed e¤ect leading to the
relationship
wgd = bd0 + b1 wgd
1
+ "g ; g = 1; 2;
(8)
where wgd is the wealth level of generation g in dynasty d, bd0 is the …xed e¤ect of the dynasty and
"g is an error term. A direct estimation of equation (8) will provide an inconsistent estimate of
b1 because the assumption of strict exogeneity of the regressors is violated by construction when
using the lagged dependent variable as regressor. The Within estimator is also biased and so is
an estimation of the …rst di¤erences:
wgd = b1 wgd
where
wgd
wgd
wgd
1.
1
+
"g ;
(9)
However, our assumption that "g is serially uncorrelated allows us to
follow the empirical approach …rst suggested by Anderson and Hsiao (1982) and use grandparental
wealth wgd
2
as an instrument for
wgd
1.
This avoids the bias of the lagged dependent variable
and provides a consistent estimate of b1 . Table 8 shows the results from this exercise where we
have allowed each child-parents-grandparents to have a unique constant bd0 .15 The …rst column
reports the OLS estimate of b1 under the assumption of a common constant bd0 = b0 for d, while
the second column reports the …rst-di¤erences 2SLS estimate of b1 . The table shows that the
2SLS estimate of the coe¢ cient is only around 1/3 of the OLS estimate. Thus, allowing for …xed
e¤ects instead of a common constant reduces the estimate substantially, strongly suggesting more
persistence in wealth formation across generations and that the standard measurement of the
IWE is underestimating the level of intergenerational ‡uidity.
15
We have chosen this completely ‡exible procedure rather than, for example, restricting siblings to have the
same …xed e¤ect because they have the same family background.
24
4.6
Robustness
In the empirical analysis, we have imposed the condition that both parents of a child should be
alive in 2011 and that some grandparents should be alive in 1985. We have therefore allowed
for the possibility that grandparents die between 1985 and 2011 and leave wealth to their heirs,
and we have allowed for variation in the number of grandparents alive in 1985. In order to study
the importance of these sample selection criteria, we have redone the baseline regressions for
the subsample where all four grandparents are alive in 2011. The results are shown in Table 9.
The basic child-parents wealth elasticity equals 0.17 (0.19 before), the basic child-grandparents
elasticity is 0.06 (0.09 before) and the 2SLS estimate of the child-parents wealth elasticity is 0.52
(0.61 before). The estimates are therefore somewhat smaller, which may re‡ect the presence of
bequest in the large sample or just that individuals are younger in the subsample, but without
changing the main conclusions.
5
Concluding remarks
Using administrative wealth records, we have estimated the child-parents IWE. The theory section illuminates that the IWE is generally not a deep parameter, but a complex function of the
underlying mechanisms, by which the intergenerational transmission occurs.
However, we …nd a pronounced stability of the IWE across speci…cations, time, and generations, suggesting that parental wealth may serve as a su¢ cient statistic for the e¤ect of parental
characteristics on children’s wealth that vary across di¤erent contexts that we consider. In particular, lack of substantial sensitivity to many controls (including income and education) suggests
that the role of these speci…c channels in explaining wealth of children is captured by parental
wealth.
Exploiting that Danish administrative wealth records allow us to use data for three generations, we …nd that there is role to be played by grandparental wealth in predicting their
grandchildren’s wealth, suggesting that the wealth generating process has longer memory than
just one generation. As we discuss, an alternative interpretation of this may be that of measurement error in parental wealth, where grandparental wealth, under strong assumptions, may
serve as an instrument for parental wealth, producing a much higher IWE compared to the basic
estimate. On the other hand, grandparents may simply have a direct e¤ect on grandchildren
25
(invalidating the IV procedure). Either way, our empirical evidence illustrates the value added
from having more generations of wealth data in characterizing the process that governs wealth
across generations.
A
Additional description of the wealth data
A.1
More details on the wealth data
The wealth data records are subject to a number of data breaks due to changing classi…cations
of certain assets and liabilities, changes in reporting requirements, changes in tax treatment, etc.
Table A.1 provides an overview of all data breaks in the underlying components of assets and
liabilities. Although we do not construct the aggregate measures of assets and liabilities but
instead rely on those compiled by Statistics Denmark, the table is still informative regarding
the stability of the de…nition of wealth in the period. On the larger lines, subcomponents are
generally third-party reported since 1997, whereas they relied in part on third-party reports and
self-reporting prior to 1997.
The treatment of company values for self-employed has undergone a number of changes
since the 1980s. In the period 1981 to 1985, …rm assets such as buildings and operating …xture,
equipment, machines, and cars are included. In 1981, buildings and operating …xture, equipment,
machines, cars, etc. are registered at 80 pct. of the cash value or the balance sheet book value.
It is calculated as 75 pct. of the cash value in 1982, 70 pct. of the cash value in 1983-1988,
and 60 pct. of the cash value in 1988-1996. In the period 1986 to 1996, the equity of the …rm
is computed separately and included in the assets of a self-employed. In addition to the above
assets, the computation of …rm equity also includes …nancial assets of the …rm, inventory, etc.,
and company debt is subtracted. From 1997 only …rm assets are included in the assets of the
owner while …rm liabilities are included in the liabilities of the owner.
A.2
Analysing the impact of the 1997 change in the de…nition of wealth
The largest change in the de…nition of wealth occurs around 1997 where the wealth tax was
abolished. However, for 1995 and 1996 Statistics Denmark computed assets and liabilities of
each individual using both the new de…nition of wealth (used for children and parents) and the
old de…nition (used for grandparents). In Table A.2 and Figures A.1 and A.2 we exploit this
26
overlap to show that the new wealth measure is well approximated by the old way of measuring
wealth.
In Table A.2 we run OLS regressions of the new de…nition of wealth measured in 1995 on the
old de…nition of wealth measured also in 1995, and …xing the constant tern at zero. Columns 1
and 2 run regressions for grandparental and parental wealth, respectively, in the CPG sample,
and column 3 runs the regression for parental wealth in the CP sample.16 In all three cases, the
slope coe¢ cient is fairly close to unity, supporting our claim that the new de…nition approximates
well the old de…nition.
Figure A.1 presents scatter plots of the new de…nition plotted against the old de…nition of
wealth in 1995 for the same three cases as mentioned above. Axes are con…ned to wealth levels of
no more than
1 million DKK (in 2010-prices) for readability. Again we …nd that observations
tend to be concentrated around the 45 degree line through origo.
In Figure A.2 we show histograms of the deviations of the new de…nition of wealth in 1995
from the old de…ntion. The histograms exclude observations with no deviation and con…ne the
primary axis to discrepancies of less than
1 million DKK (in 2010-prices) for readability. The
distribution of discrepancies for all three cases are symmetric around zero and do not show any
tendency for the new de…nition to systematically over- or underpredict old de…nition wealth.
B
Estimating approximate elasticities with the inverse hyperbolic sine (IHS) transformation
The IHS transformation, de…ned as w = IHS(W ) = log W +
p
W 2 + 1 , behaves as
log(jW j),
except in a neighborhood around zero. Intuitively, we must then be able to estimate approximate
elasticities in regressions of an IHS transformed variable on another IHS transformed variable.
p
To see this, …rst note that the derivative of the IHS function is 1= W 2 + 1. The slope parameter
from regressing y = IHS(Y ) on x = IHS(X) and a constant term is given by
^ = @E [yjx] = p @Y
@E [x]
Y2+1
p
X2 + 1
@X
@Y jXj
;
@X jY j
when X and Y are not too close to zero. In practice the approximation works well for wealth
data, where the bulk of the mass of the wealth distribution is located away from zero.
16
Notice that the CP and CPG sample sizes are slightly lower than those reported in Table 1. This is due to
observations with missing values in 1995, e.g., due to temporary emigration or, in the case of grandparents, death.
27
References
[1] Anderson, T.W. and C. Hsiao (1982). "Formulation and Estimation of Dynamic Models
Using Panel Data." Journal of Econometrics 18, 47–82.
[2] Arrondel, Luc (2009). "My Father Was Right: The Transmission of Values between Generations." PSE Working Paper 2009-12.
[3] Atkinson, Anthony B., Thomas Piketty and Emmanuel Saez (2011). "Top Incomes in the
Long Run of History." Journal of Economic Literature, 49, 3–71.
[4] Becker, Gary and Nigel Tomes (1979). “An Equilibrium Theory of the Distribution of Income
and Intergenerational Mobility.” Journal of Political Economy 87, 1153 - 89.
[5] Becker, Gary and Nigel Tomes (1986). “Human Capital and the Rise and Fall of Families.”
Journal of Labor Economics 4, 1-39.
[6] Björklund, Anders and Jännti, Markus (2009). "Intergenerational Income Mobility and the
Role of Family Background." in W. Salverda, B. Nolan and T. Smeeding, eds., Oxford
Handbook of Economic Inequality, Oxford: Oxford University Press, 491-521.
[7] Black, Sandra and Paul J. Devereux (2011). "Recent Developments in Intergenerational
Mobility." In: Ashenfelter, Orley, Card, David (Eds.), Handbook of Labor Economics. Vol.
IVb. North-Holland, Amsterdam, 1487–1541.
[8] Bound, John, David A. Jaeger and Regina M. Baker (1995). "Problems with Instrumental
Variables Estimation When the Correlation Between the Instruments and the Endogeneous
Explanatory Variable is Weak." Journal of the American Statistical Association 90, 443-450.
[9] Charles, Kerwin K., Hurst, Erik (2003). "The Correlation of Wealth Across Generations."
The Journal of Political Economy 111, 1155–1182.
[10] Chetty, Raj, John N. Friedman and Tore Olsen and Luigi Pistaferri (2011). "Adjustment
Costs, Firm Responses, and Micro vs. Macro Labor Supply Elasticities: Evidence from
Danish Tax Records." Quarterly Journal of Economics, 126(2), 749-804.
28
[11] European Commission (2012). "Alert mechanism report." http://ec.europa.eu/economy_
finance/economic_governance/documents/alert_mechanism_report_2012_en.pdf.
[12] Goldberger, Arthur S. (1989). "Economic and Mechanical Models of Intergenerational Transmission." American Economic Review 79, 504-513.
[13] Haider, Steven and Gary Solon (2006). "Life-Cycle Variation in the Association between
Current and Lifetime Earnings." American Economic Review 96, 1308–1320.
[14] International Monetary Fund (2012). "World Economic Outlook (WEO): Growth Resuming,
Dangers Remain." April 2012 (Washington).
[15] Kleven, Henrik Jacobsen, Martin Knudsen, Claus Thustrup Kreiner, Søren Pedersen and
Emmanuel Saez (2011). "Unwilling or Unable to Cheat? Evidence from a Tax Audit Experiment in Denmark." Econometrica 79, 651–692.
[16] Kreiner, Claus Thustrup, David Dreyer Lassen and Søren Leth-Petersen (2012). "Measuring
the Accuracy of Survey Responses using Administrative Register Data: Evidence from Denmark." Manuscript prepared for "Improving the Measurement of Household Consumption
Expenditures," eds. Christopher Carroll, Thomas Crossley and John Sabelhaus. Forthcoming
NBER Book Series Studies in Income and Wealth.
[17] Kolodziejczyk, Christophe (2011). "The Intergenerational Correlation of Wealth and Portfolio Allocation." Unpublished working paper.
[18] Leth-Petersen, Søren (2010). "Intertemporal Consumption and Credit Constraints: Does
Consumption Respond to An Exogenous Shock to Credit?" American Economic Review,
100(3), pp. 1080-1103.
[19] Mazumder, Bhashkar (2005). "Fortunate sons: new estimates of intergenerational mobility
in the US using social security earnings data." Review of Economics and Statistics 87, 235255.
[20] Piketty, Thomas (2000). "Theories of Persistent Inequality and Intergenerational Mobility."
In: Atkinson, A.B. and F. Bourguignon (Eds.), Handbook of Income Distribution. Vol I.
North-Holland, Amsterdam, 430–476.
29
[21] Piketty, Thomas (2011). "On the Long-Run Evolution of Inheritance: France 1820–2050."
Quarterly Journal of Economics 126, 1071-1131.
[22] Solon, Gary (1992). "Intergenerational income mobility in the United States." American
Economic Review 82, 393–408.
[23] Solon, Gary (1999). "Intergenerational mobility in the labor market." In: Ashenfelter, Orley,
Card, David (Eds.), Handbook of Labor Economics. Vol III. North-Holland, Amsterdam,
1761–1800.
[24] Solon, Gary (2012). "Theoretical Models of Inequality Transmission across Multiple Generations." Working paper. Michigan State University.
[25] Stiglitz, Joseph E. (1969). "Distribution of Income and Wealth Among Individuals." Econometrica 37, 382-397.
30
Table 1: Summary Statistics
Child-Parent (CP) Sample
Child-Parent-Grandparent (CPG) Sample
Children
2009-2011
Parents
1997-1999
Children
2009-2011
Parents
1997-1999
Grandparents
1983-1985
33.9
(8.2)
12.9
(2.4)
256,025
(207,597)
326,867
(233,078)
0.22
(0.41)
0.47
(0.50)
0.06
(0.23)
0.04
(0.19)
655,952
(1,988,246)
636,575
(1,702,573)
19,377
(1,117,250)
48.5
(7.6)
12.3
(2.6)
288,873
(174,194)
396,203
(345,531)
0.26
(0.36)
0.59
(0.34)
0.06
(0.19)
0.08
(0.20)
923,242
(2,413,591)
596,021
(1,207,167)
327,220
(1,928,688)
23.4
(2.3)
11.0
(1.7)
129,398
(103,486)
172,004
(92,620)
0.15
(0.36)
0.11
(0.32)
0.03
(0.16)
0.01
(0.10)
95,113
(367,708)
129,221
(343,321)
-34,108
(215,500)
35.0
(2.2)
12.6
(1.9)
282,080
(135,885)
358,322
(127,748)
0.14
(0.28)
0.59
(0.41)
0.01
(0.08)
0.06
(0.17)
584,975
(883,319)
605,768
(714,934)
-20,793
(536,283)
47.1
(5.1)
8.9
(2.3)
247,334
(133,734)
371,134
(163,437)
0.07
(0.14)
0.41
(0.23)
0.11
(0.20)
0.11
(0.16)
828,626
(1,094,917)
550,996
(822,594)
277,894
(701,004)
Percentiles of wealth
20th
40th
60th
80th
-232,694
-68,913
8,240
147,696
-89,456
47,364
255,708
585,444
-90,626
-24,166
3,969
28,575
-185,697
-87,330
-14,398
123,348
-10,472
111,541
273,039
499,783
Observations
1,155,564
1,155,564
97,438
97,438
97,438
Age
Years of educationa
Labor income
Gross income
Share owning stocks
Share owning propertyb
Share owning bondsc
Share self-employedd
Value of assets
Value of liabilities
Net wealth
Notes: The table reports mean values and standard deviations (in parentheses) of the variables. Age, education and ownership variables
are as of 2011 for children, 1998 for parents and 1983 for grandparents.
Child-Parent (CP) sample: Children are aged 21-51 in 2011, both parents are alive in 2011 and aged 21-66 in 1999, and children are
neither immigrants nor descendants of immigrants.
Child-Parents-Grandparents (CPG) sample: Children are aged 19-51 in 2011, both parents are alive in 2011 and aged 21-39 in 1999,
children are neither immigrants nor descendants of immigrants, and have at least one grandparent alive in 1983. Parent variables are
averages of biological parents. Grandparent variables are averages of biological grandparents. All monetary variables are measured in
DKK and deflated with 2010 prices.
a) Measures years of completed education. The variable is based on 2010 data for children.
b) Property ownership dummy for grandparents is based on 1987 data.
c) Bond ownership dummy for grandparents is based on 1995 data.
d) Self-employed dummy for children is based on 2010 data.
Table 2: Child-Parent Wealth Elasticity
(1)
Child wealth
2009-2011
log
Parental per cap. wealth
0.379
(1997-1999, log)
(0.002)
(2)
Child wealth
2009-2011
log
0.268
(3)
Child wealth
2009-2011
IHS
(4)
Child wealth
2009-2011
IHS
0.268
0.190
(0.002)
(0.001)
(0.002)
Parental per cap. wealth
(1997-1999, IHS)
Child age dummies
X
X
X
Parental age (avg.,
rounded) dummies
Observations
R-squared
Adj. R-squared
X
X
X
385,338
0.267
0.267
385,338
0.268
0.267
1,155,564
0.102
0.102
385,338
0.086
0.086
Notes: All regressions are on the CP sample described in Table 1. Difference in number of observations from (1)-(2) to (4)
is that the log transform in (1)-(2) excludes observations of zero or negative wealth. The regression in (3) is run on the same
sample as in (1)-(2). Robust standard errors are reported in the parentheses.
Table 3: Child-Parent Wealth Elasticity and the Importance of Own and Parental Income.
(1)
(2)
(3)
(4)
(5)
Baseline
Par. age <=
Par. age > 50
50
Parental per cap.
0.190
0.186
0.175
0.165
0.185
wealth 1997-1999
(0.001)
(0.001)
(0.001)
(0.001)
(0.002)
Child income
2009-2011
1.354
1.134
-0.299
2.772
(0.022)
(0.022)
(0.027)
(0.035)
2.215
3.057
1.276
(0.029)
(0.041)
(0.042)
Parental per cap.
income 1997-1999
Child age dummies
X
X
X
X
X
Parental age (avg.,
rounded) dummies
Observations
R-squared
Adj. R-squared
X
X
X
X
X
1,155,564
0.102
0.102
1,155,564
0.105
0.105
1,155,564
0.110
0.110
611,918
0.147
0.147
543,646
0.067
0.067
Notes: Dependent variable is the average 2009-2011 wealth of children. The IHS transformation is used on wealth and
income variables. All regressions are on the CP sample described in Table 1. Robust standard errors are reported in the
parentheses.
Columns (4) and (5) split the sample by median parental age (50 in 1999).
Table 4: Child-Parent Wealth Elasticity and the Importance of Controls.
(1)
(2)
(3)
(4)
Parental per cap.
0.190
0.183
0.173
0.141
wealth 1997-1999
(0.001)
(0.001)
(0.001)
(0.001)
(5)
0.133
(6)
0.134
(0.001)
(0.001)
Child income
2009-2011
-0.407
(0.023)
Parental per cap.
income 1997-1999
0.671
(0.033)
X
No. of siblings
dummiesa
X
X
X
X
X
X
X
Years of schooling
dummiesb
Financial
composition
dummiesc
Child age and
parental age
dummies
Observations
R-squared
Adj. R-squared
X
X
X
X
X
X
X
1,155,564
0.102
0.102
1,155,564
0.105
0.105
1,155,564
0.111
0.111
1,155,564
0.155
0.155
1,155,564
0.161
0.161
1,155,564
0.162
0.162
Notes: Dependent variable is the average 2009-2011 wealth of children. The IHS transformation is used on wealth and
income variables. All regressions are on the CP sample described in Table 1. Robust standard errors are reported in the
parentheses.
a) No. of siblings is calculated as the average of mother's no. of children and father's no. of children (rounded).
b) Years of schooling dummies for both child and parent are included. Years of schooling is recorded as of 2010.
c) Financial composition consists of dummies for both child and parents for homeownership, stock ownership, bonds
ownership, and for being self-employed. All dummies are included for both child and parents. Parents are noted as owning
stocks, say, if at least one parent owns stocks. Self-employment status for children is taken in 2010.
Table 5: Child-Parent and Child-Grandparent Wealth Elasticities
(1)
(2)
Child wealth
Parental per cap.
2009-2011
wealth
1997-1999
Parental per cap. wealth
0.177
1997-1999
(0.003)
Grandparental per cap.
wealth 1983-1985
Child age dummies
X
Parental age (avg.,
rounded) dummies
X
Grandparent age (avg.,
rounded) dummies
Observations
R-squared
Adj. R-squared
97,438
0.194
0.194
(3)
Child wealth
2009-2011
(4)
Child wealth
2009-2011
0.168
(0.003)
0.160
0.094
0.062
(0.003)
(0.003)
(0.003)
X
X
X
X
X
X
X
97,438
0.055
0.055
97,438
0.161
0.160
97,438
0.200
0.199
Notes: The IHS transformation is used on wealth variables. All regressions are on the CPG sample described in Table 1.
Robust standard errors are reported in the parentheses.
Table 6: Child-Parent and Child-Grandparent Wealth Elasticities, Including Various Control Variables.
(1)
(2)
(3)
Child wealth
Child wealth
Child wealth
2009-2011
2009-2011
2009-2011
Parental per cap. wealth
0.168
0.161
0.126
1997-1999
(0.003)
(0.003)
(0.003)
Grandparental per cap. wealth
1983-1985
0.062
0.054
0.038
(0.003)
(0.003)
(0.003)
No. of siblings dummiesa
X
X
Number of cousins dummiesb
X
X
Number of living grandparents in
2011 dummiesc
X
X
Years of schooling dummiesd
X
Financial composition dummiese
X
Full set of age dummies
Observations
R-squared
Adj. R-squared
X
97,438
0.200
0.199
X
97,438
0.206
0.205
X
97,438
0.256
0.255
Notes: The IHS transformation is used on wealth and income variables. All regressions are on the CPG sample described in
Table 1. Robust standard errors are reported in the parentheses.
a) No. of siblings is calculated as the average of mother's no. of children and father's no. of children (rounded).
b) No. of cousins is calculated as the average of the (at most) four grandparents' no. of grandchildren (rounded).
c) Al combinations of four dummies (one for each grandparent) denoting whether a grandparent is alive in 2011.
d) Years of schooling dummies for both child and parent are included. Years of schooling is recorded as of 2010.
e) Financial composition consists of dummies for both child and parents for homeownership, stock ownership, bonds
ownership, and for being self-employed. All dummies are included for both child and parents. Parents are noted as owning
stocks, say, if at least one parent owns stocks. Self-employment status for children is taken in 2010.
Table 7: Child-Parent Wealth Elasticities, 2SLS Estimation Using Grandparental Wealth As
Instrument.
(1)
(2)
(3)
(4)
(5)
(6)
1st stage
2nd stage
1st stage
2nd stage
1st stage
2nd stage
IV
IV
IV
IV
IV
IV
Grandparental per
0.155
0.151
0.087
cap. wealth
1983-1985
(0.003)
(0.003)
(0.003)
Parental per cap.
wealth 1997-1999
0.608
0.603
0.631
(0.022)
(0.023)
(0.040)
Number of siblings
dummies
X
X
X
X
Number of cousins
dummies
X
X
X
X
X
X
97,438
0.182
0.181
700.42
0.0000
97,438
0.016
0.015
Extra control
variables*
Observations
R-squared
Adj. R-squared
F-test (1st stage)
F-test p.-val. (1st
stage)
Partial R-sq (1st
stage)
R-sq (1st stage)
Adj. R-sq (1st
stage)
97,438
0.067
0.067
2,097.88
0.0000
97,438
.
.
97,438
0.074
0.073
1,976.82
0.0000
97,438
.
.
0.0186
0.0176
0.0064
0.0670
0.0667
0.0739
0.0732
0.1819
0.1809
Notes: The IHS transformation is used on wealth and income variables. All regressions are on the CPG sample described
in Table 1. Robust standard errors are reported in the parentheses. All regressions include both child and parental age
dummies.
*The extra control variables used are identical to the ones in regression (6) of Table 4.
Table 8: Wealth Elasticities With Child Fixed Effects.
(1)
OLS
Parental per cap. Wealth
0.220
1997-1999
(0.003)
Observations
97,438
R-squared
0.055
(2)
FD 2SLS
0.080
(0.005)
97,438
.
Notes: Dependent variable is the average 2009-2011 wealth of children. The IHS transformation is used on wealth variables.
All regressions are on the CPG sample described in Table 1. Robust standard errors are reported in the parentheses.
Estimation details: OLS estimation of child wealth regressed on parental wealth and a constant. FD 2SLS is the difference
between child and parents regressed on the difference between parents and grandparents, where the difference between
parents and grandparents is instrumented using grandparental (i.e., double lagged) per capita wealth.
Table 9: Child-Parent Wealth Elasticities, Robustness Check Using Families With 4 Living
Grandparents.
(1)
(2)
(3)
(4)
OLS
OLS
1st stage IV
2nd stage IV
Parental per cap. wealth
0.165
0.521
1997-1999
(0.006)
(0.062)
Grandparental per cap.
wealth 1983-1985
Child age dummies
X
Parental age (avg.,
rounded) dummies
X
Grandparent age (avg.,
rounded) dummies
Observations
R-squared
Adj. R-squared
F-test (1st stage)
F-test p.-val. (1st stage)
Partial R-sq (1st stage)
R-sq (1st stage)
Adj. R-sq (1st stage)
0.059
0.137
(0.008)
(0.009)
X
X
X
X
X
15,091
0.069
0.068
246.61
0.0000
0.0147
0.0692
0.0675
15,091
0.042
0.040
X
24,383
0.193
0.192
15,091
0.166
0.163
Notes: The IHS transformation is used on wealth variables. The results of the regression in column 1 correspond to column
4 of table 2 but now using only families with 4 living grandparents in 2011. Likewise the results in column 2 correspond to
column 3 of table 5 and results in column 3 and 4 correspond to column 1 and 2 of table 7. Robust standard errors are
reported in parentheses.
Table A.1: Wealth Data Documentation
Assets
Bank deposits
Bonds
Deeds
Stocks
Value of property
Liabilities
Bank debt
Mortgage debt
Deed debt
Year
80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 Variables
(*=ends with akt)
INDESTPI/ BANK*
a
b c
d
KURSOBL/ INDESTPI/ OBL*
a
e
f
g
KURSPANT/ INDESTPI/ PANT*
a
h e
d
KURS*
a
i
d
g
KOEJD/ KOEJD_NY05
j
a
k
a,l
a,o
a,o
m
n
p
n
n
n
q
r
o
d
d
d
(*=ends with GALD, GAELD or GÆLD)
GÆLDIO/ BANK*/ PRI*/ BANK*
PRI*/ OBL*
PRI*/ PANT*/ BANK*/ PANT*
Color coding:
Combined 3rd party reporting and self reporting
3rd party reports
Variable overlap
Variable shift
Data breaks
a During 1984-1986, not incl. people with special income; Income from stocks and bonds, self-employed, or income from other countries. From 1987 and onwards everyone is included.
b Including market value of bonds.
c Including deeds in deposits.
d Wealth tax is abolished. Only 3rd party info. from financial institutions and banks is available.
e Included in the aggregate variable indestpi. No seperate registration.
f Wealth tax is abolished. Only 3rd party info. from financial institutions and banks is available. Only incl. bonds in deposits.
g From 2001 the part of a mutual fond placed in bonds is moved from KURSAKT to OBLAKT.
h Only incl. deeds in deposits.
i Excl. unlisted stocks from 1994-1996.
j Value of property is for 500,000 people only registered in the aggregate asset variable, QAKTIVF.
k KOEJD only includes residential property, KOEJD_NY05 also includes business property and undeveloped land.
l Included in the aggregate variable GÆLDIO, which includes all other debt (including debt to foreign countries) than mortgage debt. No separate registration.
m Independent registration of debt to financial institutions. Deeds issued by financial institutions is included.
n During 1987-1993 debt in own business is not included in BANKGAELD. From 1990 and onwards including debt in The Mortgage Bank, pension funds, insurance and financial companies, credit and debit card
debt. From 1991 including student debt in financial institutions. From 1993 including debt in deposited deeds (PANTGALD). The variable does not exist in 1994, bank debt is only registrered as part of the aggregate
variable PRIGÆLD.
o No separate registration. Variable included in the aggregate variable PRIGÆLD.
p During 1987-1993 deed debt in own business is not included in PANTGALD.
q From 1992 excluding debt in deeds, which are not deposited.
r Debt in deposited deeds is included in the variable BANKGAELD and later PRIGÆLD. No separate registration.
Table A.2: Wealth Data Break 1995, New Definition Regressed On Old Definition.
Grandparental wealth
CPG sample
(1)
(2)
Grandparental wealth
Parental wealth
0.923
CP sample
(3)
Parental wealth
(0.001)
Parental wealth
0.889
0.875
Observations
R-squared
Adj. R-squared
(0.001)
97,388
0.794
0.794
(0.000)
1,155,090
0.771
0.771
97,328
0.855
0.855
Notes: Dependent variable is the new definition of wealth. Regressions in column 1-2 are on the CPG sample described in
Table 1. The regression in column 3 is on the CP sample described in Table 1. The difference in sample size compared to
Table 1 is due to missing values of 1995 wealth. The IHS transformation is used on wealth variables.
The constant term is fixed at zero. Robust standard errors are reported in the parentheses.
Notes: Estimates of the parent-child elasticity of wealth stem from separate regressions of child wealth (2009-2011,
IHS) on parental per cap. wealth (1997-1999, IHS) and parental age (avg., rounded) dummies by child age in 2011.
The regressions are run on the CP sample described in Table 1. 95 percent confidence bounds are calculated using
robust standard errors.
Notes: Estimates of the parent-child elasticity of wealth stem from separate regressions of child wealth (2009-2011,
IHS) on parental per cap. wealth (1997-1999, IHS) and child age dummies by age of parents (avg., rounded) at
childbirth. The sample used is the CP sample described in Table 1. 95 percent confidence bounds are calculated
using robust standard errors.
Notes: Estimates of the parent-child elasticity of wealth stem from separate regressions of child wealth (2009-2011,
IHS) on parental per cap. wealth (1997-1999, IHS) and parental age (avg., rounded) dummies by child age in 2011
using 2SLS and OLS. For 2SLS, grandparental wealth (1983-1985, IHS) and a second degree polynomial in
grandparental age (avg., rounded) are used to instrument for parental wealth. OLS regressions are run on the CP
sample (described in Table 1), and the 2SLS regressions are run on the CPG sample. 2SLS estimates are shown for
child ages for which the first stage regression is strong, meaning that the F-test for joint exclusion of the instruments
has an F-value above 10 and a p-value below 0.05. OLS estimates are shown for the same ages. 95 percent
confidence bounds are calculated using robust standard errors.
Notes: Estimates of the parent-child elasticity of wealth stem from separate regressions of child wealth (2009-2011,
IHS) on parental per cap. wealth (1997-1999, IHS) and child age dummies by age of parents (avg., rounded) at
childbirth using 2SLS and OLS. For 2SLS, grandparental wealth (1983-1985, IHS) and a second degree polynomial
in grandparental age (avg., rounded) are used to instrument for parental wealth. OLS regressions are run on the CP
sample (described in Table 1), and the 2SLS regressions are run on the CPG sample. 2SLS estimates are shown for
parental ages (at childbirth) for which the first stage regression is strong, meaning that the F-test for joint exclusion
of the instruments has an F-value above 10 and a p-value below 0.05. OLS estimates are shown for the same ages.
95 percent confidence bounds are calculated using robust standard errors.
Figure A.1: Analysis of the Wealth Data Break in 1995. Scatter plots of individual wealth as recorded by the new definition plotted against wealth as
recorded by the old definition. Panel (a) and (b) show the plot for grandparents and parents, respectively, in the CPG sample. Panel (c) shows the plot for
parents in the CP sample. Sample sizes differ compared to those in Table 1 due to missing observations in 1995, e.g. grandparents dying before 1995, and
as we only show observations not exceeding ±1 million DKK (in 2010-prices).
Figure A.2: Analysis of the Wealth Data Break in 1995. Histograms of the difference in wealth as measured by the new and old definitions. Panel (a) and
(b) show the histograms for grandparents and parents, respectively, in the CPG sample. Panel (c) shows the plot for parents in the CP sample. Sample sizes
differ compared to those in Table 1 due to missing observations in 1995, e.g. grandparents dying before 1995, as we only show observations with
discrepancies not exceeding ±1 million DKK (in 2010-prices), and as we likewise exclude observations with no discrepancy.